SALEN: Structural Archimedean Non–Coverage in Canonically Anchored Obstruction Systems

We study periodic obstruction systems acting on a discrete axis, in which each modulus induces forbidden classes in a rigid way, with no freedom of translation. In this setting we introduce and formalize the SALEN principle (Strong Archimedean Local Eventual Non-Coverage), which asserts that finite families of canonically anchored obstructions cannot cover arbitrarily long contiguous intervals beyond an explicit archimedean scale. We isolate a precise structural hypothesis, called bounded local multiplicity, under which SALEN holds as a theorem with linear scale. The proof is completely deterministic and geometric, relying only on canonical anchoring, exact counting, and elementary properties of arithmetic progressions, without the use of probabilistic arguments, density estimates, or asymptotic analysis. We further show that bounded local multiplicity is automatically satisfied in canonically indexed obstruction systems, which makes SALEN a closed structural result independent of any specific arithmetic interpretation. The work establishes SALEN as a reusable non-coverage principle, intended to be used as a black-box input in subsequent developments.